Cremona's table of elliptic curves

175 = 5² · 7

Field	Data	Notes
Atkin-Lehner	5+ 7+	Signs for the Atkin-Lehner involutions
Class	175b	Isogeny class
Conductor	175	Conductor
∏ cp	4	Product of Tamagawa factors cp
Δ	-669921875 = -1 · 59 · 73	Discriminant
Eigenvalues	0 -1 5+ 7+ -3 -5 -3  2	Hecke eigenvalues for primes up to 20
Equation	[0,-1,1,217,-282]	[a1,a2,a3,a4,a6]
Generators	[12:62:1]	Generators of the group modulo torsion
j	71991296/42875	j-invariant
L	1.0476202635275	L(r)(E,1)/r!
Ω	0.94305438771256	Real period
R	0.27772000140643	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	2800s2 11200c2 1575e2 35a1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 175b2

a2	a3	a5	a7	a11	a13	a17	a19	a23	a29	a31	a37	a41	a43	a47	a53	a59	a61	a67	a71	a73	a79	a83	a89	a97
0	-1	+	+	-3	-5	-3	2	6	3	-4	-2	-12	10	-9	-12	0	8	4	0	-2	-1	-12	-12	1

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Quadratic twists for elliptic curve 175b2

-4	8	-3	5	-7	-11	13	17	-19	-23
2800s2	11200c2	1575e2	35a1	1225a2	21175r2	29575h2	50575m2	63175d2	92575n2

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Data from Elliptic Curve Data by J. E. Cremona.
Design inspired by The Modular Forms Explorer by William Stein.

Part of Computational Number Theory
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